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In this paper, we comment on the recent comparison in Azzalini et al. (2014)of two different distributions proposed in the literature for the modelling ofdata that have asymmetric and possibly long-tailed clusters. They are referredto as the restricted and unrestricted skew t-distributions by Lee and McLachlan(2013a). Firstly, we wish to point out that in Lee and McLachlan (2014b), whichpreceded this comparison, it is shown how a distribution belonging to thebroader class, the canonical fundamental skew t (CFUST) class, can be fittedwith essentially no additional computational effort than for the unrestricteddistribution. The CFUST class includes the restricted and unrestricteddistributions as special cases. Thus the user now has the option of letting thedata decide as to which model is appropriate for their particular dataset.Secondly, we wish to identify several statements in the comparison by Azzaliniet al.(2014) that demonstrate a serious misunderstanding of the reporting ofresults in Lee and McLachlan (2014a) on the relative performance of these twoskew t-distributions. In particular, there is an apparent misunderstanding ofthe nomenclature that has been adopted to distinguish between these two models.Thirdly, we take the opportunity to report here that we have obtained improvedfits, in some cases a marked improvement, for the unrestricted model forvarious cases corresponding to different combinations of the variables in thetwo real datasets that were used in Azzalini et al. (2014) to mount theirclaims on the relative superiority of the restricted and unrestricted models.For one case the misclassification rate of our fit under the unrestricted modelis less than one third of their reported error rate. Our results thus reversetheir claims on the ranking of the restricted and unrestricted models in suchcases.

Comment on "Comparing two formulations of skew distributions with  special reference to model-based clustering" by A. Azzalini, R. Browne, M.  Genton, and P. McNicholas